Fuzzy TOPSIS - Análise de Ações

Bibliotecas

# Instalar as bibliotecas equivalentes no Python
!pip install pandas numpy matplotlib seaborn scikit-learn yfinance statsmodels openpyxl prophet

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Download dos Dados

# Importar as bibliotecas equivalentes no Python
import pandas as pd           # Manipulação de dados
import numpy as np            # Operações matemáticas
import matplotlib.pyplot as plt  # Gráficos
import seaborn as sns         # Gráficos
import yfinance as yf         # Dados de ações
from statsmodels.tsa.api import ExponentialSmoothing, ARIMA # Modelos de séries temporais
import statsmodels.api as sm  # Modelagem estatística geral
from prophet import Prophet   # Previsão de séries temporais
import datetime               # Manipulação de datas
import openpyxl               # Leitura e escrita de arquivos Excel

Tickers da carteira

import yfinance as yf
import pandas as pd
import numpy as np
from datetime import datetime, timedelta
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
import matplotlib.pyplot as plt

# 1) Configuração inicial
tickers = ['BRFS3.SA', 'JBSS3.SA', 'BEEF3.SA', 'MRFG3.SA', 'TSN', 'HRL', 'GIS']
start_date = '2020-01-01'
n_ahead = 22
window = 20

# 2) Baixa preços e calcula log-retornos
prices_list = [yf.download(ticker, start=start_date)['Close'] for ticker in tickers]
portfolioPrices = pd.concat(prices_list, axis=1)
portfolioPrices.columns = tickers
portfolioPrices = portfolioPrices.dropna()

log_returns = np.log(portfolioPrices / portfolioPrices.shift(1)).dropna().reset_index()
log_returns = log_returns.rename(columns={'Date': 'date'})

# 3) Modelagem Linear com "quebras" (polynomial regression por ativo)
log_returns_long = log_returns.melt(id_vars='date', var_name='asset', value_name='ret')
log_returns_long['trend'] = log_returns_long.groupby('asset').cumcount()

fitted_list = []

for asset in tickers:
    df_asset = log_returns_long[log_returns_long['asset'] == asset].copy()
    poly = PolynomialFeatures(degree=2)
    X_poly = poly.fit_transform(df_asset[['trend']])
    model = LinearRegression().fit(X_poly, df_asset['ret'])
    df_asset['fitted'] = model.predict(X_poly)
    fitted_list.append(df_asset)

log_returns_long = pd.concat(fitted_list, ignore_index=True)

# 4) Próximos 22 dias úteis
last_date = log_returns_long['date'].max()
future_dates = pd.bdate_range(start=last_date + timedelta(days=1), periods=n_ahead)
future_tsbl = pd.DataFrame({
    'date': np.tile(future_dates, len(tickers)),
    'asset': np.repeat(tickers, n_ahead)
})

# 5) Simula 3 cenários de retorno (bootstrap)
# 5) Simula 3 cenários de retorno (bootstrap)
np.random.seed(1234)
sims_all = []

for i in range(3):
    sim_list = []
    for asset in tickers:
        returns = log_returns_long.loc[log_returns_long['asset'] == asset, 'ret']
        sim_returns = np.random.choice(returns, size=n_ahead, replace=True)
        sim_df = pd.DataFrame({
            'date': future_dates,
            'asset': asset,
            'ret': sim_returns,
            '.rep': f'sim{i+1}'
        })
        sim_list.append(sim_df)
    sims_all.append(pd.concat(sim_list))

sims_all = pd.concat(sims_all, ignore_index=True)


# 7) Volatilidade móvel
ret_all = sims_all.sort_values(['asset', '.rep', 'date'])
ret_all['vol'] = ret_all.groupby(['asset', '.rep'])['ret'].transform(lambda x: x.rolling(window).std())

# Exibir os primeiros dados para verificação
ret_all.head()

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	date	asset	ret	.rep	vol
44	2025-06-13	BEEF3.SA	0.001519	sim1	NaN
45	2025-06-16	BEEF3.SA	0.011852	sim1	NaN
46	2025-06-17	BEEF3.SA	-0.024015	sim1	NaN
47	2025-06-18	BEEF3.SA	-0.004181	sim1	NaN
48	2025-06-19	BEEF3.SA	-0.003175	sim1	NaN

Download dos preços históricos

import seaborn as sns
import matplotlib.pyplot as plt

# Definir paleta de cores e estilos personalizados
custom_palette = {
    'hist': 'red',
    'sim1': 'green',
    'sim2': 'blue',
    'sim3': 'purple'
}

custom_linestyles = {
    'hist': 'solid',
    'sim1': 'dotted',
    'sim2': 'dashed',
    'sim3': (0, (3, 1, 1, 1))  # dash-dot
}

# Gráfico de Retornos (Histórico + Simulações)
g = sns.FacetGrid(
    ret_all,
    col="asset",
    col_wrap=2,
    height=3.5,
    sharey=False,
    aspect=1.5,
    palette=custom_palette
)

# Função para aplicar estilo e cor no gráfico
def plot_line(data, color, **kwargs):
    for rep in data['.rep'].unique():
        subset = data[data['.rep'] == rep]
        plt.plot(
            subset['date'], subset['ret'],
            label=rep,
            linestyle=custom_linestyles.get(rep, 'solid'),
            linewidth=0.7,
            color=custom_palette.get(rep, color)
        )

g.map_dataframe(plot_line)

# Ajustar o eixo e títulos
g.set_axis_labels("Data", "Log-retorno")
g.set_titles("{col_name}")

# Rotacionar o eixo x
for ax in g.axes.flat:
    ax.tick_params(axis='x', rotation=45)

# Título geral
g.fig.suptitle(f"Retornos: Histórico (252 dias) & {n_ahead} Simulações", fontsize=14)

# Ajustar a legenda final
handles, labels = g.axes[0].get_legend_handles_labels()
g.fig.legend(handles, labels, title="Cenário", loc='lower center', ncol=4)
plt.subplots_adjust(top=0.88, bottom=0.12)

plt.show()

Verificação dos dados baixados

import seaborn as sns
import matplotlib.pyplot as plt

# Definir paleta de cores e estilos para cada cenário
custom_palette = {
    'hist': 'red',
    'sim1': 'green',
    'sim2': 'blue',
    'sim3': 'purple'
}

custom_linestyles = {
    'hist': 'solid',
    'sim1': 'dotted',
    'sim2': 'dashed',
    'sim3': (0, (3, 1, 1, 1))  # dash-dot
}

# Gráfico 2: Volatilidade Móvel (Histórico + Simulações)
g = sns.FacetGrid(
    ret_all,
    col="asset",
    col_wrap=2,
    height=3.5,
    sharey=False,
    aspect=1.5
)

# Função para aplicar estilo e cor no gráfico
def plot_line(data, color, **kwargs):
    for rep in data['.rep'].unique():
        subset = data[data['.rep'] == rep]
        plt.plot(
            subset['date'], subset['vol'],
            label=rep,
            linestyle=custom_linestyles.get(rep, 'solid'),
            linewidth=0.7,
            color=custom_palette.get(rep, color)
        )

g.map_dataframe(plot_line)

# Ajustar o eixo e títulos
g.set_axis_labels("Data", f"Desvio-padrão móvel ({window} dias)")
g.set_titles("{col_name}")

# Rotacionar o eixo x
for ax in g.axes.flat:
    ax.tick_params(axis='x', rotation=45)

# Título geral
g.fig.suptitle(f"Volatilidade Móvel ({window} dias): Histórico & Simulações", fontsize=14)

# Ajustar a legenda final
handles, labels = g.axes[0].get_legend_handles_labels()
g.fig.legend(handles, labels, title="Cenário", loc='lower center', ncol=4)
plt.subplots_adjust(top=0.88, bottom=0.12)

plt.show()

Preparação dos Dados

import pandas as pd
from openpyxl import Workbook
from openpyxl.utils.dataframe import dataframe_to_rows
from openpyxl.styles import numbers

# 8) Exporta Excel com uma aba por cenário
wb = Workbook()
wb.remove(wb.active)  # Remove aba padrão

for sc in ret_all['.rep'].unique():
    df = ret_all[ret_all['.rep'] == sc].copy()

    # Pivotar como no R
    df = df[['date', 'asset', 'ret', 'vol']]
    df_long = df.melt(id_vars=['date', 'asset'], var_name='metric', value_name='value')
    df_long['col'] = df_long['metric'] + '_' + df_long['asset']
    df_wide = df_long.pivot_table(index='date', columns='col', values='value').reset_index()
    df_wide = df_wide.sort_values('date')

    # Criar aba e adicionar dados
    ws = wb.create_sheet(title=sc)
    for r in dataframe_to_rows(df_wide, index=False, header=True):
        ws.append(r)

    # Formatar colunas numéricas
    for col in ws.iter_cols(min_row=2, min_col=2):
        for cell in col:
            cell.number_format = '#,##0.00'

# Salvar o arquivo
wb.save("retornos_e_volatilidades.xlsx")

Cálculo de Retornos

# Instala dependências
!pip install -q PyPortfolioOpt pandas numpy openpyxl plotly scipy

import pandas as pd
import numpy as np
from scipy.stats import dirichlet
import plotly.graph_objs as go
from plotly.subplots import make_subplots

# 1) Parâmetros Monte Carlo
N_PORTFOLIOS = 50_000
RISK_FREE    = 0.0

# 2) Carrega Excel e cenários
xls    = pd.ExcelFile("retornos_e_volatilidades.xlsx")
sheets = xls.sheet_names  # ["hist","sim1","sim2","sim3"]

# 3) Prepara figura Plotly 2×2
fig = make_subplots(
    rows=2, cols=2,
    subplot_titles=[f"Cenário {sc}" for sc in sheets],
    horizontal_spacing=0.1, vertical_spacing=0.15
)

# 4) Loop: simulações, frontier e MaxSharpe
for idx, sc in enumerate(sheets):
    # cálculo de linha/col
    row = idx//2 + 1
    col = idx%2 + 1

    # 4.1) Retornos do cenário
    df   = pd.read_excel(xls, sheet_name=sc, index_col=0, parse_dates=True)
    rets = (
        df.filter(regex="^ret_")
          .rename(columns=lambda c:c.replace("ret_",""))
          .replace([np.inf,-np.inf], np.nan)
          .dropna(axis=1, how="any")
    )
    tickers = rets.columns.tolist()
    mu  = rets.mean()
    cov = rets.cov()

    # 4.2) Simula carteiras
    W = np.random.dirichlet(np.ones(len(tickers)), size=N_PORTFOLIOS)
    port_rets  = W.dot(mu.values)
    port_vars  = np.einsum('ij,jk,ik->i', W, cov.values, W)
    port_risks = np.sqrt(port_vars)

    # 4.3) Max Sharpe
    sharpe = (port_rets - RISK_FREE) / port_risks
    idx_sh  = np.nanargmax(sharpe)
    opt_ret  = port_rets[idx_sh]
    opt_risk = port_risks[idx_sh]

    # 4.4) Fronteira eficiente empírica
    df_mc   = pd.DataFrame({"risk":port_risks, "ret":port_rets})
    df_mc   = df_mc.sort_values("ret")
    frontier = []
    min_r = np.inf
    for r, q in zip(df_mc["risk"], df_mc["ret"]):
        if r < min_r:
            frontier.append((r,q))
            min_r = r
    frontier = np.array(frontier)

    # 4.5) Adiciona traces a cada subplot
    fig.add_trace(
        go.Scatter(
            x=df_mc["risk"], y=df_mc["ret"],
            mode="markers",
            marker=dict(size=2, opacity=0.15, color="gray"),
            name="Simulações",
            showlegend=(idx==0)
        ),
        row, col
    )
    fig.add_trace(
        go.Scatter(
            x=frontier[:,0], y=frontier[:,1],
            mode="lines",
            line=dict(color="red", width=2),
            name="Fronteira",
            showlegend=(idx==0)
        ),
        row, col
    )
    fig.add_trace(
        go.Scatter(
            x=[opt_risk], y=[opt_ret],
            mode="markers",
            marker=dict(symbol="star", size=14, color="gold"),
            name="Máx Sharpe",
            showlegend=(idx==0)
        ),
        row, col
    )

    # 4.6) Ajusta eixos
    fig.update_xaxes(title_text="Risco σ", row=row, col=col)
    fig.update_yaxes(title_text="Retorno Exp.", row=row, col=col)

# 5) Layout geral
fig.update_layout(
    height=800, width=900,
    title_text="Fronteiras Eficientes (Monte Carlo) e Máx Sharpe por Cenário",
    legend=dict(x=0.85, y=0.05)
)

# 6) Exibe
fig.show()

Normalização e Pesos (Fuzzy TOPSIS)

# 1) Instala dependências
!pip install -q scipy pandas numpy openpyxl matplotlib

# 2) Imports
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import differential_evolution

# 3) Carrega os retornos simulados do cenário "sim1"
xls = pd.ExcelFile("retornos_e_volatilidades.xlsx")
df  = pd.read_excel(xls, sheet_name="sim1", index_col=0, parse_dates=True)

# 4) Extrai apenas as colunas de retorno
rets = (df
        .filter(regex="^ret_")
        .rename(columns=lambda c: c.replace("ret_",""))
        .replace([np.inf, -np.inf], np.nan)
        .dropna(axis=1, how="any"))

tickers = rets.columns.tolist()
n = len(tickers)

# 5) Estatísticas de Markowitz
mu    = rets.mean().values        # retornos médios diários
Sigma = rets.cov().values         # covariância diária

# 6) Parâmetros de alocação mínima
min_w = 0.05                      # cada ativo tem no mínimo 5%
scale = 1 - n * min_w             # parte restante para distribuir

gamma = 1.0                       # trade-off risco vs retorno

# 7) Função‐objetivo (risk - γ·return)
def markowitz_obj(x):
    # x em [0,1]^n  →  w_i ≥ min_w, soma(w)=1
    raw = np.abs(x)
    if raw.sum() == 0:
        raw = np.ones_like(raw)
    w = min_w + scale * raw / raw.sum()
    ret  = mu.dot(w)
    risk = np.sqrt(w @ Sigma @ w)
    return risk - gamma * ret

# 8) Bounds para DE em [0,1]
bounds = [(0,1)] * n

# 9) Executa Differential Evolution
res = differential_evolution(
    markowitz_obj,
    bounds,
    strategy     = 'best1bin',
    popsize      = 15,
    mutation     = (0.5, 1),
    recombination= 0.7,
    tol          = 1e-6,
    maxiter      = 1000,
    polish       = True,
    seed         = 42
)

# 10) Transforma o vetor X em pesos w
x_opt = np.abs(res.x)
w_opt = min_w + scale * x_opt / x_opt.sum()

# 11) Calcula métricas finais
port_ret   = mu.dot(w_opt)
port_risk  = np.sqrt(w_opt @ Sigma @ w_opt)
sharpe     = port_ret / port_risk

# 12) Exibe resultados
print(f"\n=== Alocação Ótima (Markowitz via DE) — cenário sim1 ===\n")
for tkr, w in zip(tickers, w_opt):
    print(f"  {tkr:10s}: {w*100:6.2f}%")
print(f"\nRetorno Esperado Diário: {port_ret:.4f}")
print(f"Risco (σ diário)       : {port_risk:.4f}")
print(f"Sharpe Ratio (Rf=0)    : {sharpe:.4f}")

import plotly.express as px

# 1) Monte um DataFrame de pesos
df_w = pd.DataFrame({
    "Ativo": tickers,
    "Peso": w_opt
})

# 2) Gera o gráfico de barras interativo
fig = px.bar(
    df_w,
    x="Ativo",
    y="Peso",
    title="Alocação Ótima de Ativos — sim1",
    text=df_w["Peso"].apply(lambda x: f"{x*100:.2f}%")
)

# 3) Ajustes finos
fig.update_traces(
    marker_color="green",
    textposition="outside"
)
fig.update_layout(
    yaxis=dict(title="Peso (%)", tickformat=".1%"),
    xaxis_tickangle=-45,
    uniformtext_minsize=8,
    uniformtext_mode="hide"
)

# 4) Exibe
fig.show()

=== Alocação Ótima (Markowitz via DE) — cenário sim1 ===

  BEEF3.SA  :   5.00%
  BRFS3.SA  :   5.00%
  GIS       :  30.45%
  HRL       :  33.92%
  JBSS3.SA  :   9.47%
  MRFG3.SA  :  11.15%
  TSN       :   5.00%

Retorno Esperado Diário: 0.0010
Risco (σ diário)       : 0.0072
Sharpe Ratio (Rf=0)    : 0.1384

Cálculo do TOPSIS

# 1) Imports (supondo que já tenha numpy, pandas, plotly instalados)

import numpy as np
import plotly.graph_objs as go
from plotly.subplots import make_subplots

# 2) Carrega retornos simulados do cenário "sim1"
xls    = pd.ExcelFile("retornos_e_volatilidades.xlsx")
df     = pd.read_excel(xls, sheet_name="sim1", index_col=0, parse_dates=True)
rets   = (df
           .filter(regex="^ret_")
           .rename(columns=lambda c: c.replace("ret_",""))
           .replace([np.inf,-np.inf], np.nan)
           .dropna(axis=1, how="any"))

# 3) Vetor de pesos 'w_opt' já calculado anteriormente
#    Exemplo: w_opt = np.array([...]) na mesma ordem de rets.columns
weights = pd.Series(w_opt, index=rets.columns)

# 4) Série de retornos da carteira
port_ret = rets.dot(weights)

# 5) Performance cumulativa (índice de riqueza)
#    W₀ = 1, W_t = ∏_{i=1}^t (1 + r_i)
wealth = (1 + port_ret).cumprod()

# 6) Drawdown
#    DD_t = (W_t - max_{s≤t} W_s) / max_{s≤t} W_s
running_max = wealth.cummax()
drawdown    = (wealth - running_max) / running_max
max_dd      = drawdown.min()

# 7) Monta gráfico interativo com Plotly
fig = make_subplots(
    rows=2, cols=1, shared_xaxes=True,
    row_heights=[0.6, 0.4],
    subplot_titles=[
        "Performance Cumulativa da Carteira Ótima (sim1)",
        f"Drawdown Diário (Máx: {max_dd:.2%})"
    ]
)

# 7.1) Wealth index
fig.add_trace(
    go.Scatter(
        x=wealth.index, y=wealth.values,
        mode="lines", name="Wealth Index"
    ),
    row=1, col=1
)

# 7.2) Drawdown
fig.add_trace(
    go.Scatter(
        x=drawdown.index, y=drawdown.values,
        mode="lines", name="Drawdown",
        fill='tozeroy', line=dict(color='crimson')
    ),
    row=2, col=1
)

# 8) Layout
fig.update_yaxes(title_text="Índice de Riqueza", row=1, col=1)
fig.update_yaxes(title_text="Drawdown", row=2, col=1, tickformat=".0%")
fig.update_xaxes(title_text="Data", row=2, col=1)

fig.update_layout(
    height=600, width=800,
    showlegend=False,
    title_text="Performance e Drawdown da Carteira Ótima — sim1"
)

fig.show()

Resultado Final